150822742857 · 2503# + 1633050373
At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important PrimePages database: a collection of research, records and results all about prime numbers. This page summarizes our information about one of these primes.
This prime's information:
| Description: | 150822742857 · 2503# + 1633050373 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Consecutive primes arithmetic progression (5,d=30) |
| Proof-code(s): (*): | x38 : Broadhurst, OpenPFGW, Primo |
| Decimal Digits: | 1072 (log10 is 1071.477174448) |
| Rank (*): | 128408 (digit rank is 27) |
| Entrance Rank (*): | 103537 |
| Currently on list? (*): | no |
| Submitted: | 11/19/2013 20:00:08 UTC |
| Last modified: | 2/4/2026 11:16:07 UTC |
| Database id: | 116360 |
| Status Flags: | none |
| Score (*): | 25.4879 (normalized score 0) |
Archival tags:
There are certain forms classed as archivable: these prime may (at times) remain on this list even if they do not make the Top 5000 proper. Such primes are tracked with archival tags.
- Consecutive Primes in Arithmetic Progression (archivable class *)
- Prime on list: no, rank 14
Subcategory: "5/5"
(archival tag id 238857, tag last modified 2025-02-16 14:52:00)- Arithmetic Progressions of Primes (archivable class *)
- Prime on list: no, rank 174, weight 37.532251874718
Subcategory: "5/5"
(archival tag id 235389, tag last modified 2025-04-02 08:37:18)
Verification data:
The Top 5000 Primes is a list for proven primes only. In order to maintain the integrity of this list, we seek to verify the primality of all submissions. We are currently unable to check all proofs (ECPP, KP, ...), but we will at least trial divide and PRP check every entry before it is included in the list.
field value prime_id 116360 person_id 9 machine Using: Digital Ocean Droplet what prime notes PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 150822742857*2503#+1633050373 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000002306211862.txt
trial
Running N-1 test using base 2
Generic modular reduction using generic reduction FMA3 FFT length 384 on A 3560-bit number
Running N-1 test using base 3
Generic modular reduction using generic reduction FMA3 FFT length 384 on A 3560-bit number
Running N+1 test using discriminant 11, base 1+sqrt(11)
Generic modular reduction using generic reduction FMA3 FFT length 384 on A 3560-bit number
Calling N-1 BLS with factored part 100.00% and helper 0.70% (300.73% proof)
150822742857*2503#+1633050373 is prime! (0.0869s+0.0002s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
95717
52243723135305236219408449389303083...(1066 digits)...40916817537461056057436129067878671
103
146009modified 2026-02-04 11:16:07 created 2026-02-04 11:16:02 id 187726
field value prime_id 116360 person_id 9 machine Ditto P4 P4 what prp notes Command: /home/ditto/client/pfgw -tc -q"150822742857*2503#+1633050373" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 150822742857*2503#+1633050373 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 5, base 1+sqrt(5) Calling N+1 BLS with factored part 0.70% and helper 0.53% (2.70% proof) 150822742857*2503#+1633050373 is Fermat and Lucas PRP! (0.3483s+0.0003s) [Elapsed time: 1.00 seconds] modified 2020-07-07 22:30:18 created 2013-11-19 20:08:03 id 161867
Query times: 0.0032 seconds to select prime, 0.004 seconds to seek comments.
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